Use the given root to find the solution set of the polynomial.
Polynomial: x^4 - 4x^3 + 2x^2 - 4x + 1 = 0
Given root: i
How do I solve this problem?
Hi tsmith,
If one of the roots is i, then one of the roots is also -i.
(x - i) and (x + i) are factors.
Their product is $\displaystyle x^2+1$
Use polynomial long division on your original function to find the depressed quadratic.
I think you'll discover it's $\displaystyle x^2-4x+1$
Now, use the quadratic formula to discover the last two roots.